Home » Courses » Course 447: Applied Kalman Filtering with Emphasis on GPS-Aided Systems Print Page

Course 447: Applied Kalman Filtering with Emphasis on GPS-Aided Systems

Course 447 Backround Image

Course 447: Applied Kalman Filtering with Emphasis on GPS-Aided Systems

Instructor: Mr. Michael Vaujin, Consultant
2.4 CEUs
Onsite onlyOur most requested courses are offered at different public venues two to three times per year. Most of our courses also can be taught onsite at your location. Most on-site courses can be customized to your needs. Read more about our on-site course options.

Course Description

This is a highly intensive 4-day short course on Kalman filtering theory and Kalman filtering applications. Included is a discussion of linear, extended, unscented, and square root Kalman filters and their practical applications to real-time strapdown navigation and target tracking. Exposure to Information filters, 2nd and 3rd order extended Kalman filters, particle filters, integrity monitoring, and methods of smoothing is included. Emphasis is on practical applications, but sufficient supporting theory is provided for further research. Designed for engineers who need a working knowledge of Kalman filtering or who work in the fields of navigation or target tracking.

Objectives

  • The student will receive a thorough understanding of linear, extended, unscented, and square root Kalman filters and their practical applications to real time strapdown navigation and target tracking. The student will also be exposed to Information filters, 2nd and 3rd order extended Kalman filters, particle filters, integrity monitoring, and methods of smoothing.
  • Emphasis is on practical applications, but sufficient supporting theory is provided to give attendees the necessary tools for meaningful research and development work in the field. Considerable time is devoted to modeling, the most difficult aspect of Kalman filtering, in an application setting.
  • There will be a high level of instructor/attendee interaction, designed to provide hands-on problem solving and solution discussions.

Prerequisites

  • A basic understanding of linear systems.
  • A basic understanding of probability, random variables, and stochastic processes.
  • A thorough familiarity with matrix algebra principles.

Who Should Attend?

  • Engineers who need a working knowledge of Kalman Filtering or who work in the fields of either navigation or target tracking.

Equipment You Should Bring

  • A laptop (PC or Mac) with full version of MATLAB 5.0 (or later) installed. This will allow you to work the problems in class and do the practice "homework" problems each evening. All of the problems will also be worked in class by the instructor, so this equipment is not required, but is recommended. These course notes are searchable and you can take electronic notes with the Adobe Acrobat 9 Reader we will provide you.

Materials You Will Keep

  • A color electronic copy of all course notes will be provided on a USB Drive or CD-ROM. Bringing a laptop to this class is highly recommended; power access will be provided.
  • A black and white hard copy of the course notes will also be provided.
  • Public Venue Attendees: Introduction to Random Signals and Applied Kalman Filtering, 3rd edition, by R. Grover Brown and Patrick Hwang, John Wiley & Sons, Inc., 1996. (Note: This arrangement does not apply to on-site contracts. Any books for on-site group contracts are negotiated on a case by case basis.)

Morning

Random Process Review

  • Random variables, probability densities, Gaussian and multivariate
  • Expectation, covariance matrix, random process, autocorrelation, power spectral density, stationary and nonstationary
  • Linear response, shaping filters

State Space Modeling

  • Models derived from differential equations, PSDs and block diagrams
  • Discrete time solution
  • Mean and covariance response
  • Markov and integrated Markov examples
  • Transition and process covariance

Random Process Simulation and Analysis

  • Vector random process simulation
  • Autocorrelation and PSD from data
  • Markov random process modeling and design
  • Computer demo

 

Afternoon

KF System Integration

  • Integration with complementary filtering
  • Integration examples
  • State space modeling
  • Simplified KF derivation

The Kalman Filter

  • Simplified algorithm description
  • Bias, random walk and Markov examples
  • Off-line error (covariance) analysis

Alternate Kalman Algorithms

  • State augmentation
  • Sequential processing
  • Known control inputs
  • Generalized KFs for correlated noises
  • LU decorrelation
  • Matrix partitioning for efficiency
Course: 557
Remote Course, December 2021

I would definitely recommend this course to any of my colleagues in the navigation areas!

— Soren Knutson, BAE Systems
Course: 346
Remote Course, November 2021

The teaching style was very good. Dr. Hegarty was very effective at taking a massive amount of information and presenting it in a clear and well-paced manner even with the challenge of the virtual format.

— Ryan Burgess, US Army
Course: 557
Remote Course, December 2021

It is easy to tell that this course is taught by passionate instructors, and that comes through both in their mastery of the subject material, and enthusiasm in presenting the subject matter in a concise and easy-to-follow manner. Despite the difficulty of the material, this course is one of the most well-taught courses I’ve had the pleasure of taking. I urge both of the instructors to keep teaching, as an instructor’s passion is instrumental in a student’s absorption of material. Needless to say, they both have passion in spades.

— Aaron Bruinsma, L3 Harris Wescam
Course: 335
Remote Course, May 2021

Dr. Betz teaching style is engaging and he encourages class participation versus a monologue. Dr. Betz also makes a point to review previous material before presenting new material so the student has the opportunity to close any gaps on understanding any of the material.

— Military Attendee, Name Withheld Upon Request, US Military
Course: 335
Remote Course, May 2021

My objectives were “to learn more about GPS in general, jamming, receiver’s performance measures like C/No and J/S. Yes, the course met the objectives more than expected.”

— Military Attendee, Name Withheld Upon Request, US Military
Course: 335
Remote Course, May 2021

Quality of all course initiatives were great. Schedule, instructor/attendee interaction, and user friendliness were all great.

— Military Attendee, Name Withheld Upon Request, US Military
Course: 551
Remote Course, April 2021

Very effective class and I enjoyed it from the beginning to the end.

— Liangchun Xu, Samsung
Course: 346
Remote Course, April 2021

I am an electrical engineer who has recently started a new job in the GPS world and was looking for a course to learn GPS fundamentals to be quickly brought up to speed. My objectives were exceeded because Dr. Hegarty did a fantastic job explaining GPS fundamentals with lots of nods at electrical engineers, but most importantly, shared his invaluable practical knowledge from 30 years working in this field!

— Marie-Michèle Siu, Canadian Forces
Course: 346
Remote Course, April 2021

Chris is very clear in explaining topics at hand and allows for questions when things are unclear. Even in this digital form it was an interactive course.

— Alexander Haagsma, NLR
Course: 122
Remote Course, April 2021

The teaching style was very good, it was easy to follow the class even for non-native English speakers.

— Virginia Antón, ESSP SAS
Scroll to Top